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In arXiv:2307.03503 [math.NA] we commenced to study a variant of theRaviart-Thomas mixed finite element method for triangles, to solve second orderelliptic equations in a curved domain with Neumann or mixed boundaryconditions. It is well known that in such a case the normal component of theflux variable should not take up values at nodes shifted to the boundary of theapproximating polytope in the corresponding normal direction. This is becausethe method's accuracy downgrades, which was shown in previous work by the firstauthor et al. An order-preserving technique was studied therein, based on aparametric version of these elements with curved simplexes. Our variant is analternative to the approach advocated in those articles, allowing to achievethe same effect with straight-edged triangles. The key point of this method isa Petrov-Galerkin formulation of the mixed problem, in which the test-fluxspace is a little different from the shape-flux space. In this paper we firstrecall the description of this method, together with underlying uniformstability results given in arXiv:2307.03503 [math.NA]. Then we show that itgives rise to optimal-order interpolation in the space H(div). Accordingly apriori error estimates are obtained for the Poisson equation taken as a model.

A variant of the Raviart-Thomas method to handle smooth domains using straight-edged triangles. Part II -- Approximation results